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Number of positive integers `x` for which `f(x)=x^3-8x^2+20 x-13` is a prime number is______.

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RESONANCE ENGLISH-NUMBER THEORY-Exercise -1 (PART - I)
  1. Find remainder when 4444^(4444) is divided by 9

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  2. Find the smallest natural number n which has last digit 6 & if this la...

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  3. Does there exist an integer such that its cube is equal to 3n^(2) + 3n...

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  4. For how many integers n is sqrt(9-(n+2)^2) a real number?

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  5. The number of prime numbers less than 1 million whose digital sum is 2...

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  6. An eight digit number is a multiple of 73 and 137. If the second digit...

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  7. The number of natural numbers n for which (15n^2+8n+6)/n is a natural...

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  8. Let A be the least number such that 10A is a perfect square and 35 A i...

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  9. The number of 2 digit numbers having exactly 6 factors is :

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  10. The number of positive integers 'n' for which 3n-4, 4n-5 and 5n - 3 a...

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  11. Number of positive integers x for which f(x)=x^3-8x^2+20 x-13 is a pri...

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  12. a, b, c are digits of a 3-digit number such that 64a + 8b + c = 403, t...

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  13. N is a five digit number. 1 is written after the 5 digit of N to make ...

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  14. The sum of all values of integers n for which (n^2-9)/(n-1) is also an...

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  15. The number of natural number pairs (x, y) in which x gt y and 5/x+6/y...

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  16. The number of positive integer pairs (a, b) such that ab - 24 = 2a is

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  17. A = (2+ 1) (22 + 1) (2 + 1)..... (2^(2048) + 1) The value of (A + 1)^(...

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  18. The least positive integer n such that 2015^(n) + 2016^(n) + 2017^(n) ...

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  19. The four digit number 8ab9 is a perfect square. The value of a^(2) + b...

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  20. a, b are positive real numbers such that 1/a+9/b=1 The smallest value ...

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